p1 = Polygon@{{0, 0}, {5, 0}, {0, 5}};
p2 = Polygon@{{0, 0}, {5, 0}, {0, 6}};
! RegionDisjoint[p1, p2]

p1 = Polygon@{{0, 0}, {0, 5}, {5, 0}};
p2 = Polygon@{{0, 0}, {0, 5}, {5, 0}};
! RegionDisjoint[p1, p2]

p1 = Polygon@{{0, 0}, {5, 0}, {0, 5}};
p2 = Polygon@{{-10, 0}, {-5, 0}, {-1, 6}};
! RegionDisjoint[p1, p2]

p1 = Polygon@{{0, 0}, {5, 0}, {2.5, 5}};
p2 = Polygon@{{0, 4}, {2.5, -1}, {5, 4}};
! RegionDisjoint[p1, p2]

p1 = Polygon@{{0, 0}, {1, 1}, {0, 2}};
p2 = Polygon@{{2, 1}, {3, 0}, {3, 2}};
! RegionDisjoint[p1, p2]

p1 = Polygon@{{0, 0}, {1, 1}, {0, 2}};
p2 = Polygon@{{2, 1}, {3, -2}, {3, 4}};
! RegionDisjoint[p1, p2]

p1 = Polygon@{{0, 0}, {1, 0}, {0, 1}};
p2 = Polygon@{{1, 0}, {2, 0}, {1, 1}};
! RegionDisjoint[p1, p2]